While racing on a flat track, a car rounds a curve of 56 m radius and instantaneously experiences a centripetal acceleration of 36 m/s2. How fast was the car going?
I know the answer i s45 I just need to know why ASAP!!!!!!!!!!!!!!!!!!!!
a = v^2/r
ar = v^2
56*36 = v^2
2016 = v^2
v = 44.9
To determine how fast the car was going, we can use the formula for centripetal acceleration:
a = (v^2) / r
Where:
- a is the centripetal acceleration
- v is the velocity of the car
- r is the radius of the curve
We are given that the centripetal acceleration is 36 m/s^2, and the radius of the curve is 56 m. We need to find the velocity.
Rearranging the formula, we get:
v^2 = a * r
Substituting the given values:
v^2 = 36 m/s^2 * 56 m
Now we can solve for v by taking the square root of both sides:
v = √(36 m/s^2 * 56 m)
v ≈ 45 m/s
Therefore, the car was going approximately 45 m/s.
To find the speed at which the car was going while rounding the curve, we can use the formula for centripetal acceleration:
a = (v^2) / r
Where:
a = centripetal acceleration (given as 36 m/s^2)
v = speed of the car
r = radius of the curve (given as 56 m)
Rearranging the formula to solve for v:
v = sqrt(a * r)
Plugging in the given values:
v = sqrt(36 * 56)
v = sqrt(2016)
v ≈ 44.9 m/s
Therefore, the speed of the car was approximately 44.9 m/s or rounded to the nearest whole number, 45 m/s.